1157
I n d . Eng. Chem. Res. 1991,30, 1157-1165
Registry No. A, 122-79-2; B, 1575-87-7; C, 2937-64-6; 38782-65-9; E, 2937-70-4; F, 2219-90-1; G, 132492-03-6; 132492-04-7; (PhOH)(HCOH) (copolymer), 9003-35-4.
D, H,
Literature Cited Andreis, M.; Koenig, J. L. Application of NMR to Crosslinked Systems. Polymer CharacterizationlPolymer Solutions; Advances in Polymer Science No. 89; Springer-Verlag: New York, 1989. Bersted, B. H. Polymer Characterization/Polymer Solutions. J. Polym. Sci. 1973, 17, 1415-30. Florv. P. J. Princides of Polymer Chemistry: Cornel1 University Piess, Ithaca, NY, 1953. Ford, W. T.; Balakrishnan, T. 13C NMR Spectra of Cross-Linked Polv(stvrene-co-chloromethvlstvrene) Gels. In Polymer Characteri%ion; Craver, C. P.,-Ed.; American Chemical Society: Washington, DC, 1983. Fvfe. C. A.: Rudin. A.: Tchir. W. ADDlication of Hieh-Resolution 13C " NMR Spectroscopy Using Magic' Angle Spinniig Techniques to the Direct Investigation of Solid Cured Phenolic Resins. Macromolecules 1980, 13, 1320-2. Gollob, L.; Krahmer, R. L.; Wellons, J. D.; Christiansen, A. W. Relationship Between Chemical Characteristics of Phenol-Formaldehyde Resins and Adhesive Performance. For. Prod. J. 1985, 35 (3), 42-8.
Kamide, K.; Miyakawa, Y. Limiting Viscosity Number-Molecular Weight Relationships for Phenol-Formaldehyde Resin in Solution. Makromol. Chem. 1978,179,359-72. Kelusky, E. C.; Fyfe, C. A.; McKinnon, M. S. Investigation of the Curing of Phenolic Resins by 2D NMR Spectroscopy. Macromolecules 1986, 19, 329-32. Kim, M. G.; Amos, L. W.; Barnes, E. E. Study of the Reaction Rates and Structures of a Phenol-Formaldehyde Resol Resin by Car-
bon-13 NMR and Gel Permeation Chromatography. Znd. Eng. Chem. Res. 1990,29, 2032-7. Longi, P.; Greco, F.; Rossi, U. Polymers Containing Intra-Molecular Crosslinks. Makromol. Chem. 1969, 129, 15764. Maciel, G. E.; ODonnell, D. J.; Ackerman, J. J. H.; Hawkins, B. L.; Bartuska, V. J. A 13C NMR Study of Four Lignins in the Solid and Solution State. Makromol. Chem. 1981,182,2297-304. Maciel, G. E.; Chuang, I.; Gollob, L. Solid-state 13C NMR Study of Resol-Type Phenol-Formaldehyde Resins. Macromolecules 1984, 17, 1081-7.
Megson, N. J. Phenolic Resin Chemistry; Academic Press: New York, 1958. Perico, A.; Rossi, C. Intrinsic Viscosity of Short Chains. I. Extension of the Theory of Kirkwood and Riseman. J. Chem. Phys. 1970, 53 (3), 1217-27.
Sojka, A. S.; Wolfe, R. A.; Dietz, E. A.; Dannels, B. F. Carbon-13 NMR of Phenolic Resins. Macromolecules 1979, 12, 767-70. Tobiason, F. L.; Chandler, C.; Schwarz, F. E. Molecular Weight-Intrinsic Viscosity Relationships for Phenol-Formaldehyde Novolak Resins. Macromolecules 1972,5, 321-5. Tobiason, F. L.; Chandler, C.; Negstad, P. Molecular Weight Characterization of Resol Phenol-Formaldehyde Resins; Advances in Chemistry Series No. 125; American Chemical Society: Washington, DC, 1973; pp 194-206. Woodbrey, J. C.; Higginbottom, H. P.; Culbertson, H. M. Proton Magnetic Resonance Study on the Structures of Phenol-Formaldehyde Resins. J. Polym. Sci. 1965, A3, 1079-106. Wooten, A. L.; Prewitt, M. L.; Sellers, T., Jr.; Teller, D. C. Gel Filtration Chromatography of Resol Phenolic Resins. J. Chromatogr. 1988,445, 371-6. Received for review March 19, 1990 Revised manuscript received July 6, 1990 Accepted November 26, 1990
PROCESS ENGINEERING AND DESIGN Reactor Simulation Studies of Methane Oxidative Coupling on a Na/NiTi03 Catalyst Jesus M.Santamaria,?Eduardo E. M i r o , t and Eduardo E. Wolf* Chemical Engineering Department, University of Notre Dame, Notre Dame, Indiana 46556
A reactor-reaction model for the oxidative coupling of methane on a 1.6% Na/NiTi03 catalyst has been developed. The reaction was assumed to take place both in the gas phase and on the catalytic surface. Kinetic rate constants experimentally obtained under differential conditions were used in a four-species kinetic model. Simulation solutions of the external field and particle equations for the temperature and concentrations were achieved by using the orthogonal collocation method combined with a Runge-Kutta procedure. The model predicted fairly well integral experimental results under various reaction conditions, and it was used to investigate the effect of several operating variables on the conversion and selectivity obtained in the methane oxidative coupling process. A simulated distributed oxygen feed system was found to improve hydrocarbon selectivity and yield at the reactor exit. Introduction In the past decade, the oxidative coupling of methane to ethane, ethylene, and higher hydrocarbons has attracted
* To whom correspondence should be addressed. 'Present address: Department of Chemical ~ ~ ~ University of Zaragoza, 5009 Zaragoza, Spain. $ Present addrese: INCAPE, Universidad Nacional del Litoral, Sgo.de1 Estero 2829 3000 Santa Fe, Argentina. 0888-5885/91/2630-ll57$02.50/0
the a t t e n t i o n of m a n y laboratories in the world, as evidenced b y the number of review papers on the subject (i.e., Bhasin, 1988;Scurrel, 1987; Lee and Oyama, 1988). In s p i t e of t h i s effort, m a n y aspects of the catalyzed process are not yet well understood, and the highest yield reported ini the literature ~ ~ up~to date ~ (about i 25%) ~ is ~Still too , low to m a k e the process commercially feasible.
Several experimental studies have been reported on the development of active and selective catalysts for the 0 1991 American Chemical Society
1158 Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991
methane coupling reaction. However only a few studies have been made with the aim of optimizing the reactions conditions for a given catalyst (Iwamatsu and Aika, 1989; Deboy and Hicks, 1988). Since the oxidative coupling of methane has been demonstrated to be an homogeneousheterogeneous reaction (Labinger and Ott, 1987; Sinev et al., 1987; Lane and Wolf, 1988), it is clear that reactor design factors and operating conditions have a fundamental importance in the achievement of higher hydrocarbon yields. Lane and Wolf (1988) determined the experimental conditions in which the noncatalyzed gas-phase reaction becomes important and also determined the kinetics of the reaction. On subsequent studies the heterogeneous catalyzed reactions have been studied on a series of alkalimetal-promoted Ti02 (Lane et al., 1989a), on various titanate catalysts (Lane et al., 1989b),and on nickel titanate (Miro et al., 1990a,b). Detailed kinetics results for a 1.6% Na/NiTi03 catalyst, obtained under conditions where gas-phase reactions are not important, have been reported by Miro et al. (1990~).Reaction engineering considerations reported to date have been focused on kinetic modeling (Labinger and Ott, 1987; Iwamatsu and Aika, 1989) and on the importance of mass-transfer restrictions (Follmer et al., 1989). Improvements in reactor design to overcome the intrinsic limitations of the gas-phase reactions have been reported by Loo et al. (1988) and Omata et al. (1989). To our knowledge, reactor analysis and modeling aspects have been largely set aside in part due to the lack of reliable kinetic results that can account for the gas-phase homogeneous reactions as well as heterogeneous reactions. The present work combines reaction engineering analysis with the experimental kinetic results previously obtained in our laboratory to predict reactor performance under various operating conditions. Model Development Kinetics of Methane Oxidative Coupling. The intense effort devoted in recent years to the investigation of methane oxidative coupling over a wide variety of catalysts has shown that the detailed reaction pathway and corresponding kinetic expression is a function of the type of catalyst used and its composition. Therefore, the approach followed when presenting kinetic results has consisted in using power law type equations. In this work, in order to emphasize the reaction engineering aspects, we have chosen to keep the kinetic model of the system as simple as poeaible, while maintaining a reasonably accurate description of the process. This can be achieved by using the following lumped kinetic model: CHA
-
!
where C2 represents the total amounts of hydrocarbons with two or more carbon atoms and CO, represents the total amount of carbon oxides. The lumping of species was required in order to reduce the number of differential equations resulting from the reactor model. The reactions are assumed to take place in the gas phase and on the catalyst surface. While it is known that C2can be oxidized in the gas phase and on the surface, independent rates for these reactions were lumped on the second pathway due to the experimental difficulty of separating both pathways. Nonetheless, the lumped kinetic expression used for CO, production does account for C2 combustion (broken line in reaction scheme). Recently, results obtained for the
gas-phase reaction under high pressure and higher conversion have been obtained independently in another laboratory (Ekstrom, 1990),confirming the validity of the rate expression obtained by Lane and Wolf (1988). Obviously, the validity of the results presented is restricted to the range of experimental conditions used, and its extrapolation far from this range must be exercised with caution due to the lumped nature of the kinetics used. The gas-phase kinetics were calculated from the results published by Lane and Wolf (1988), taking into account their reaction volume in order to refer reaction rates to the gas phase volume unit. The separate terms which appear in eqs 2 and 3 represent the formation of CO and C02and ethane and ethylene, respectively. The kinetic equations used can be written as follows (all reaction rates in kmol/(m3 s)). gas-phase kinetics
-Gdt -o , - (1.29 x -.
109)e-36100/TC 0.53C 3.70p.23 + CH,
0.622e-14%30/?'C
02
-0.95C
CH4
02
1.33p.38
(2)
-dCC, - - (5.367 x 104)e461"3/7'CCH41.04C021.78p.82 + dt (1.464 x 104)e-262@)/7'CCH41.16C0 21.627Q.78 (3) For the catalytic kinetics there is a wide variety of results to choose from in the literature. We have selected the power-law formulation of our previous results, obtained under differential conditions on a 1.6% Na/NiTi03 catalyst (Miro et al., 1990~).This catalyst, unlike other alkali-metal-loaded catalysts, displayed a stable behavior over prolonged reaction periods. Furthermore, the fact that this catalyst was available in our laboratory allowed us to check experimentally the results predicted by the simulation under integral reactor conditions. catalytic kinetics
Reactor Model. The following assumptions have been made in the simulation: 1. The catalyst pellets are spherical in shape. 2. The effective diffusivity, external heat and mass transfer coefficients, thermal conductivity, density and specific heat of both gas and solid phases remain constant independent of conversion. 3. Interparticle heat conduction and heat transfer by radiation are assumed to be less important than convective heat transport. 4. Reactor operation is plug flow and either isothermal or adiabatic. The overall oxidative coupling process is highly exothermic, and isothermal operation would be difficult to achieve in practice. However, simulation of isothermal operation was considered to be appropriate to study the influence of the changes in different operating variables without added temperature effects. Approxi-
Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 1159 mation to isothermal conditions can be achieved in fixed beds by the use of cooling devices or by operating a t low conversions or at high inert dilution ratios. With the above assumptions, the transient mass and energy equations for a packed bed reactor affected by interphase heat and mass transport between the bulk gas phase and catalyst particles can be written as follows:
aci = D,V2Ci - ri(T,Ci)
at
where Ti( T,C) now indicates catalytic reaction rate, De and k, are the effective mass and thermal diffusivities, c1 is the pellet porosity, and ps and C are the pellet density and heat capacity, respectively. f h e boundary conditions for the solution of the above equations are as follows: aCi aT 0 - - -= r=O ar ar
-
r=R where rb(T,CJ can be obtained from eqs 1-3 (or from their combination, for the case of the oxygen balance), the subscripts o and s indicate gas phase and surface conditions at the external phase of the pellets, respectively, and the subscript i denotes each of the four species considered. The boundary and initial conditions are
Cio = ciox= 0 T o = TOIF0 Cio = 0
z=o t = O
To =
Cio = -(reactants);
Ciolt -0
#io
=
(18)
with the following boundary and initial conditions:
where i = 1 for CH4, i = 2 for COX,i = 3 for C2, and i = 4 for 02. These equations can be made dimensionless by introducing the following dimensionless variables and groups: #io
a8
as = P3(B4V28 + C(AfOiri(#,e))
(94
6%)
Tolr-0
Ci = 0; T = Tolzlo (16b) These equations can be transformed into the following dimensionless form: t=O
Cio (products); CCHAr=O
TO 6, = Tolr=O
z = zz ; 7 = t Uz
f=O f = l
-
-E = Bi*(O, - 6,) st
for all 6 (19b) where the following additional dimensionless variables and groups have been used: s = o
$i
= 0,
8=1
Then eqs 7 and 8 become
where the asterisk (*) indicates that dimensionless variables are now introduced in the reaction rate expression for a particular species. The dimensionless boundary conditions are z = 0; fii0 = eio = 1 (13a) The corresponding initial conditions are t = O #io = 0; 8, = 1 for any Z (13b) Single-Particle Heat and Mass Balance. The continuity equations for the mass and heat balances in a single spherical pellet can be written as
Simultaneous solutions of the external field and particle equations for the temperature and concentrations were achieved by using the orthogonal collocation method combined with a Runge-Kutta procedure. This enabled the temperature and the concentrations of the different species to be obtained a t any point in the bed. The solution involved 16 collocation points for the reactor and 3 for the catalyst pellet. From these, methane and oxygen conversions as well as Czyield and selectivity could be calculated. The calculations were carried out on a Prime computer with computational time varying from a few minutes for the isothermal operation to about 10 min for adiabatic operation.
Experimental Section The catalyst (1.6% Na/NiTiO,) was prepared from the mixed-oxide nickel titanate (Alfa products, 99.7%), which was impregnated with a solution of sodium carbonate in
1160 Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991
E
50
2 I-
40
c
Table I. Reference Parameter Values R =2x m L = 0.2 m oxygen concentration = 16 vol % methane concentration = 32 vol % effective diffusivity = 5 X IO4 m2/s modified Sherwood number, Sh* = 500 modified Biot number, Bi* = 1.0 reactor temperature = 1073 K reactor void fraction = 0.35 total gas flow rate (STP)= IO4 m3/s effective thermal conductivity = 4 2( lo-' W/(m K)
(a)
L
'710
'
7kO
.
7iO
'
O 7;
. 760
'
7iO
'
Si0 . 8l!O
T. "C
8
4
' 6
o4
0
9
14
0, CONC Figure 1. Comparison between theoretical predictions (full lines) and experimental results (points). (a) Methane conversion and higher hydrocarbon selectivity vs temperature. (b) Methane conversion and higher hydrocarbon selectivity w oxygen concentration. Isothermal operation.
deionized water. The slurry was heated to 50 "C and the water was evaporated while stirring until a dry powder was obtained. The resulting powder was pretreated in flowing air first at 650 "C for 5 h and then at 750 "C for 2 h. The amount of sodium loading (1.6%) is defined as the initial weight of sodium divided by the sum of the weights of sodium carbonate and nickel titanate. The steady-state kinetic experiments were performed by using a single-pass flow reactor made of fused silica with an inside diameter of 0.95 cm and a heated length of 15 cm. The reaction products in the effluent stream were analyzed by a gas chromatograph equipped with Carbosphere and HayeSep Q packed columns as well as TCD/FID detectors, from which methane conversion, product selectivity, and yield were calculated. Hydrocarbon selectivity is defined as Sz+ = 2Cc,/(2Cc2 + CCO,),and hydrocarbon yield is defined as the product between selectivity and conversion.
Results and Discussion Comparison of Simulated and Experimental Reactor Performance. Before the study of the influence of the different operating and catalyst-related variables on the conversion and selectivity obtained at the reactor exit, the ability of the model (developed from differential kinetics) tQ simulate the results in a fixed bed reactor under integral conversion conditions was tested by comparing theoretical predictions with experimental results obtained in our laboratory. Such comparison is presented in Figure 1 in terms of conversion and selectivity vs temperature and oxygen concentration. A good agreement can be observed in Figure l a between the simulated conversion and selectiv-
ities (full lines) and those obtained experimentally at three different temperatures. It must be noted that the oxidative coupling kinetics were obtained independently and that there are not adjustable kinetic parameters in the model. The input operating variables (methane and oxygen inlet concentrations, reactor temperature, gas flow rate, particle size, catalyst loading),were measured directly, and the only variables to be estimated (since they were not known accurately) were those related to the physical characteristics of the catalytic system (bed porosity, particle density, effective diffusivity, and transport coefficients), whose values can only vary within a relatively narrow range. The bed porosity was estimated to be 0.35, the particle density cmz/s 1300 kg/m3, and the effective diffusivity 5 X (Satterfield and Sherwood, 1963). Transport coefficients were obtained from standard correlations for fixed beds (Wakao and Kaguei, 1982). Table I summarizes these parameters. A good agreement can be observed in Figure l a between the simulated conversion and selectivities (full lines) and those obtained experimentally at three different temperatures. The results shown in Figure l b were obtained at 800 "C and 32% CH4 inlet concentration and represent the largest deviation between theory and experiment of all the cases studied in this work. The conversion is slightly underpredicted by the model and the selectivity is slightly overpredicted; this is partly due to the fact that the power-law kinetics used for the heterogeneous catalytic results is in fact an average of the true kinetics which has been found to fit an Eley Rideal mechanism (Miro et al., 1990b,c). The isothermicity of the bed was verified experimentally with only an increase of about 2 "C in temperature along the small bed used. Yet even in this worst case, the agreement between model and experiment is quite adequate. Simulation Results. The purpose of the simulations was to study the effect of operating variables such as temperature, methane to oxygen ratio, dilution ratio, particle size, external film resistance, reactor length, reactor void fraction, and particle effective diffusivity in methane conversion and selectivity. To1 this end, the reactor was assumed to be initially at a uniform temperature, containing only the catalyst and an inert gas. A given set of inlet conditions was then imposed, and the transients were calculated until a steady state was achieved. While in general it is not always possible to extrapolate steady-state kinetics to un-steady-state kinetics, the particular catalyst used does not require the use of lattice oxygen or undergoes reduction in the absence of orygen (Miro et al., 1990b,c). Consequently, we assume that no major changes occur on the catalyst surface during transient operation and thus the kinetic expression is still valid during transient operation. In each case, the corresponding variable was changed while the other parameters were kept at their reference values, which were used in results presented in Figure 1 and are also listed in Table I, and only the departures from these values are indicated when the results
Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 1161
SELECTIVITY, S00"C 0.4
0.3
b W
'
1
0.8
-
J
: 8 W
2
0.4
Qv)
a W > f
CONV. 750°C
0.1
Conversion, L=0.2
?i 0 . 0 1
0.0 0.0
0.2
0.6
0.4
0.8
1 .o
4
F
"
6
"
8
0
'
"
10
1
12
14
16
12
14
16
0,CONC
Z Figure 2. Conversion and selectivity profiles along the reactor at two different temperatures. Isothermal conditions.
for a specific case are presented. In this paper, the sensitivity of the numerical solutions used was not studied since it was the subject of previous work done with the same numerical method (Byme et al., 1985, 1989). Influence of Temperature. For the 1.6% Na/NiTi03 in Figure la, the conversion and selectivity obtained at the reactor exit increase as reaction temperature is increased. This result stems from the predominance of the heterogeneous kinetics (Miro et al., 1990b) over the gas-phase reactions (Lane and Wolf, 1988) wherein selectivity decreases as temperature increases. It is also interesting to examine the conversion and selectivity profiles along the reactor, shown in Figure 2. In both cases, the values at 800 OC are always above those at 750 "C. Also, there is a slight increase in selectivity through the reactor (more pronounced at 800 "C), which is caused by the decrease in oxygen concentration along the bed; i.e., given the kinetic equations used in this work, the formation of CO, depends on oxygen concentration more strongly than the formation of C2both in the gas phase and on the catalyst, which means that the latter reaction is less affected by the decrease in oxygen concentration. Clearly, at temperatures higher than 800 "C the selectivity must decrease as the oxidation of C2 starts predominating. Influence of Methane and Oxygen Concentrations. Several simulations were carried out with varying oxygen feed concentrations at a constant methane feed concentration of 32%. The results are plotted in Figures 3 in terms of the conversion and selectivity obtained after a steady state is reached at the reactor exit for two different reactor lengths. It can also be seen that a noticeable decrease in selectivity is obtained when the oxygen concentration in the reactor feed is increased, which is consistent with the results presented in the previous section on the increase of selectivity along the reactor. This decrease in selectivity occurs along with an increase in methane conversion and an increase in CO, yield caused by the higher oxygen concentration. As a result of the increase in conversion, the yield to C2hydrocarbons increases with oxygen concentration, in spite of the decrease in selectivity (Figure 3b). The influence of the oxygen concentration is more clearly shown in the step experiment simulation displayed in Figure 4,in terms of dimensionless time and reactor length. A steady state was reached with 16% oxygen and 32% methane concentrations in the reactor feed (curve for time = 0). The oxygen concentration in the feed was then stepped down to 4%, and the transients were calculated until a new steady state was attained. It can be seen that
0.04
t 4
6
8
10
OXYGEN CONCENTRATION(Yo) Figure 3. Conversion and selectivity (a) and yield (b)after a steady state is reached at the reactor exit for two different reactor lengths. Isothermal conditions.
a wave of oxygen concentration profiles develops and travels down the bed until it reaches the reactor exit. This is accompanied by a front of decreasing methane conversion and increasing hydrocarbon selectivity. After the time lag for the propagation of these fronts throughout the bed (time = 130), the hydrocarbon selectivity at the reactor exit (not shown) increases until it reaches its new steady-state value (see Figure 44. The C2yield, however, decreases since the decrease in conversion overtakes the increase in selectivity. The effect of reactant dilution was tested by using different inert concentrations with the same methane to oxygen ratio. The results (not shown) are similar to those obtained when oxygen concentration is decreased; Le., the overall hydrocarbon yield increases when the concentration of the reactants in the feed is increased due to increased conversion. However, the selectivity attained at the reactor exit is practically unchanged when the concentration of reactants is reduced by as much as 50%. Influence of Internal and External Mass Transfer Resistances. Simulations were carried out for particle radii ranging from 0.5 to 3 mm. Given the above results, an increase in particle radius would be expected to produce an increase in selectivity, since it would lower the average oxygen concentration in the catalyst particle. This has in fact been already found experimentally (Follmer et al., 19891, and it is indeed shown by the simulation results (Figure 5). However, the methane conversion markedly decreases with increasing particle sizes, which results in an overall decrease in hydrocarbon yield (from 9.4% for a particle radius of 0.5 mm to 7.9% for 3 mm). The average oxygen concentration in the particle can also be decreased by using pellets of lower effective dif-
1162 Ind. Eng. Chem. Res., Vol. 30, No. 6,1991 1 .o
0.5
Dimensionless Time
z 0 Ia
0.8
I-
0.6
Y
0
0.4
W
0.2
8z
a:
z W
c 0.4 -I
8
*
ON 0.0
0.2
0.4
z
0.6
1 .o
0.8
W
> 0.1 I
I
I
I
1 e-5
2e-5
3e-5
EFFECTIVE DIFFUS IVlTY ( m2/s) Figure 6. Effect of effective diffusivity on conversion and selectivity. Isothermal conditions.
z
>
0.2
8
0 * W
g Z
0.2
a:
Conversion
9
130
0.0
0.3
I\
Selectivity
0.1
8
0
I "
0
0.0 0.0
0.2
0.4
0.6
1 .o
0.8
2 0.7
0
Dimensionless Time
6
5 a e
G
t
k 2
"I
I 0.6
0'3r
0.2 0.1
40
5 W
60
80
100
120
LENGTH
v)
Figure 7. Conversion and Selectivity as a function of reactor length under reference conditions. Isothermal conditions.
0.5
0.4 0.0
0.2
0.4
0.6
0.8
1 .o
Z Figure 4. Oxygen step simulation, from 02%= 16 (time O), to 02% = 4. (a) Oxygen concentration profiles at different dimensionless times. (b) Methane conversion profiles (c) Higher hydrocarbon selectivity profiles Isothermal conditions.
Z
0 v) U
w
>
5
0.5
1 .o
1.5
2.0
2.5
3.0
PARTICLE RADIUS, mm Figure 5. Effect of pellet size on conversion and selectivity. Isothermal conditions.
fusivity. The effects of changes in this variable over conversion and selectivity are shown in Figure 6. It can
be observed that lower diffusivities mean higher selectivities and lower conversions (and yields). Beyond approximately 3 X lo-' cm2/s, further increases in effective diffusivity do not significantly modify the conversion and selectivity obtained. A similar effect was found for the effect of the masstransfer resistance in the film surrounding the catalyst particle. Thus, a decrease of 2 orders of magnitude in the modified Shemood number (Sh*)increased the selectivity by 2.8%,at the same time reducing conversion by 10.6%. This resulted in an overall decrease of 8.1% in the yield to hydrocarbons obtained. Effect of Reactor Length. Figure 7 presents the conversion and selectivity at the reactor exit as a function of reactor length under otherwise reference conditions. Unlike the results of previous sections, in this case both conversion and selectivity increase as the reactor length is increased. This is due to the depletion of the oxygen concentration in the bed as a reactor length (and therefore the methane conversion) increases, which, as shown above, favors the selective over the nonselective reactions. However, the conversion curve and the hydrocarbon yield curve (not shown) level off for high reactor lengths, corresponding to the lower reaction rates obtained as the oxygen concentration is depleted with increased reactor length. Influence of Reactor Porosity. The influence of the gas-phase reactions has been found to impose an important limitation in the yields and selectivities obtained in methane oxidative coupling (Lane and Wolf, 1988). The model presented in this work allowed this effect to be
Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 1163 0.51
1
I
I
LL!
a
5
0.2
820
K
810
w 0.1
I
I/ ti
2 1
0.2
0.4
0.6
0.8
1 .o
0.6
0.8
1 .o
2 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
POROSITY
0.8
Figure 8. Effect of reactor porosity on conversion and selectivity. Isothermal conditions.
tested by changing the volume of gas phase in the reactor.
Figure 8 shows the variation of conversion and selectivity with reactor porosity. It can be seen that, for the conditions of this simulation, there is only a small decrease in hydrocarbon selectivity over a wide range of porosity. This is in part due to the fact that this study was carried out for a 20-cm-long reactor, which means short residence times for the gas in the bed. In any case, the main contributor to the decrease in hydrocarbon yield in this case is the drop in conversion as the volume fraction of the catalyst in the reactor is decreased. Adiabatic Operation. Since the oxidative coupling of methane is a highly exothermic process, when the reaction is carried out in an adiabatic fixed bed reactor, the characteristic high-temperature front develops and travels along the bed, increasing in magnitude with time until either a stable state or temperature runaway conditions are reached. The process of hot-spot formation and propagation is well described in the general literature on fixed bed reactors for other reaction systems, and no further results will be presented in this work concerning this point. It is, however, interesting to compare adiabatic with isothermal operation in terms of the conversion and selectivity obtained in oxidative coupling of methane. In general, the results obtained in the simulation show that the higher temperatures attained in adiabatic operation can considerably increase the conversion and selectivity of the process. This is illustrated in Figure 9, where the results obtained in adiabatic operation at a given reaction time of 63 s (this time was chosen due to limitations in computer time usage) under different conditions are compared with those for isothermal operation under reference conditions. Figure 9a shows (curve 3) the temperature profile in the reactor obtained after 63 s of reaction time with an inlet concentration of 8% oxygen. It can be seen that at this time a pronounced temperature maximum has formed and traveled approximately 25% of the reactor length. This increased temperature gives rise to a considerably higher hydrocarbon selectivity profile (Figure 9b), as compared to isothermal operation under reference conditions (curve l), and the same is true of the conversion profile along the reactor (Figure 9c). However, safety considerations as well as reactor materials impose strict limitations on the maximum temperatures that can be attained in practice. The temperature rise can be controlled by an adequate choice of operating conditions. Thus, curve 2 in Figure 9 represents the results obtained with lower reactant concentrations (4% oxygen, 8% methane), and with a higher gas flow rate (twice the reference value). A very
0.7
0.6
0.5
V.7
0.0
0.2
0.4
z
0.3 I
A
L
Figure 9. Adiabatic operation. Curve 1: isothermal operation under reference conditions. Curve 2: adiabatic operation with 8% of methane and 4% of oxygen and flow rate twice the reference value. Curve 3: adiabatic operation under reference conditons. (a) Temperature profiles. (b) Selectivity profiles. (c) Methane conversion profiles.
shallow maximum is observed in the temperature profile, which has already moved through nearly 76% of the reactor length. The selectivity obtained is higher than that under reference conditions, which is in agreement with the higher temperatures obtained. The conversion, however, is considerably lower, which means that a longer reactor would be required to obtain the same yield. Distributed Oxygen Feed. Given the strong effect of the oxygen concentration in both the conversion and selectivity obtained in oxidative coupling of methane, it seems desirable to optimize the oxygen feed to the reactor in order to maintain a relatively high conversion while avoiding the contact of the hydrocarbon products with high oxygen concentrations. In fact, membrane reactors have already been suggested (Omata et al., 1989) for the purpose of maintaining a physical separation between reaction products and the main oxygen stream. Another possibility would be to feed small amounts of oxygen at different points along the bed. This would keep a low oxygen concentration in the reactor, which, as shown above, would favor selective reactions versus deep oxidation reactions.
1164 Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991
0.7
reactor is slightly higher for the simulation performed with constant (3.008%) oxygen concentration in the bed. However, the selectivity for the constant O2concentration (Figure lob) is significantly larger than for the 8% inlet concentration. As a result, the intersection of the two curves in the yield plot (Figure 1Oc) is farther from the reactor exit, and the yield obtained for the reactor with the constant oxygen concentration is considerably higher than that for 8% inlet oxygen concentration. It is also interesting to note the fact that the trend for the hydrocarbon selectivity profile in curve 2 of Figure 10b is the inverse of that shown in the previous simulations presented in this work; i.e., the selectivity decreases along the bed. This is the variation expected when the effect of the decreasing oxygen concentration is eliminated, since the concentration of Cz hydrocarbons is increasing along the bed. Alternatively, the trends can also be explained by comparing the rate expressions which suggest that a t constant oxygen concentration selectivity to Cz decreases as methane concentration decreases. The validity of these results is constrained by the use of a lumped kinetics for COz production. Using a separate expression for C2 oxidation might affect these results.
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A reactor-reaction model for the oxidation coupling of methane on a 1.6% Na/NiTiO, catalyst has been presented. The reaction model was based on a lumped kinetics experimentally obtained under differential conditions, and predicted fairly well integral experimental results obtained with the same catalyst. The model has been used to investigate the effect of several operating variables on the conversion and selectivity obtained in the oxidative coupling process. The results of the model show that oxygen concentration is one of the main variables controlling the reactor behavior. It is also the key to avoid runaway temperature conditions. Simulation results have also shown that improvements in conversion and selectivity at the reactor exit can be obtained by modifying the way in which oxygen is fed to the reactor. Acknowledgment
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Z Figure 10. Distributed oxygen feed. Isothermal conditions. Comparison of Simulation resulta obtained with 8% of inlet oxygen concentration (1) and 3.008% of constant orygen concentration along the bed (2). (a) Methane conversion profiles. (b) Selectivity profiles. (c) Yield profiles.
T o test this approach, the oxygen concentration profile obtained at steady state with a 8% oxygen inlet concentration in a 0.8-m-long reactor was integrated to obtain the average oxygen concentration in the bed (3.008%). A simulation was then carried out in which this oxygen concentration was imposed to be constant throughout the bed. This enabled comparison of the results obtained in two reactors with the same total oxygen content but with different oxygen distribution. The results obtained at steady state are presented in Figure 10. The methane conversion profiles along the bed are shown in Figure 10a for both variable and constant oxygen concentration. It can be observed that the rate of increase of methane conversion with reactor length is initially higher for the simulation carried out with 8% oxygen inlet concentration (curve l), while the opposite is true for the second half of the reactor. The two curves intersect near the reactor exit, and the conversion obtained in the
The financial support of Amoco Research Laboratories (Naperville, IL) is gratefully acknowledged. J.M.S. is grateful to the Direccion General de Investigaciones Cientifica y Tecnica, Spain, for support as a Visiting Scholar.
Nomenclature a, = external
pellet area per unit volume of bed
Bi* = modified Biot number, R h l k , Ci= concentration of gaseous reactant i C, = specific heat De = effective diffusivity h = heat-transfer coefficient (AH) = heat of reaction k , = effective thermal conductivity of the catalyst k , = mass-transfer coefficient L = reactor length r = radial coordinate in pellet r* = reaction rate R = external radius of pellet Sh* = modified Sherwood number, Rk,/De t = time 7' = absolute temperature u = gas velocity
Ind. Eng. Chem. Res. 1991,30, 1165-1171 z = reactor length
Greek Letters t1 = pellet void fraction t2 = bed void fraction p = density Subscripts
fr = gas
= initial condition, reactant species o = bulk gas phase s = surface
I
Registry No. CH,,7482-8;Na, 7440-23-5;NiTi03, 12653-76-8.
Literature Cited Bashin, M. M. Feasibility of Ethylene Synthesis via Oxidative Coupling of Methane. Stud. Surf. Sci. Catal. 1988,36,343. Byme, A.; Hughes, R.; Santamaria, J. The Influence of Initial Coke Profile and Hydrogen Content of the Coke on the Regeneration of Fixed Beds of Catalyst. Chem. Eng. Sci. 1985,40,1507. Byme, A.; Hughes, R.; Santamaria, J. The Influence of Operating Variables on the Regeneration of Fixed Beds of Catalyst. Chem. Eng. Sci. 1989,44,2197. Deboy, J. M.;Hicks, R. F. Kinetics of the Oxidative Coupling of Methane over 1% Sr/Laz09. J. Catal. 1988,113,517. Ekstrom, A.; Regtop, R.; Bhargava, S. Effect of Pressure on the Oxidative Coupling Reaction of Methane. Appl. Catal. 1990,62, 253. Follmer, G.; Lehmann, L.; Baerns, M. Effects of Transport Limitations on Cz+Selectivity in the Oxidative Methane Coupling Reaction using NaOH/CaO Catalyst. Catal. Today 1989,4(3),323. Iwamatsu, E.; Aika,K.4. Kinetics Analysis of the Oxidative Coupling of Methane over Na+-Doped MgO. J. Catal. 1989,117,416. Labinger, J. A,; Ott, K. C. Mechanistic Studies on the Oxidative Coupling of Methane. J. Phys. Chem. 1987,91,2682.
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Lane, G. S.; Wolf, E. E. Methane Utilization by Oxidative Coupling. I. A Study of the Reaction in the Gas Phme during the cofeeding of Methane and Oxygen. J. Catal. 1988,113,144. Lane, G. S.;Miro, E. E.; Wolf, E. E. Methane Oxidative Coupling. 11. A Study of Lithium-Titania-Catalyzed Reactions of Methane. J. Catal. 1989a,119,161. Lane, G. S.; Kalenik, 2.;Wolf, E. E. Methane Oxidative Coupling over Titanate Catalysts. Appl. Catal. 1989b,53,1983. Lee, J. 5.; Oyama, S. T. Oxidative Coupling of Methane to Higher Hydrocarbons. Catal. Reu.-Sci. Eng. 1988,30(2),248. Loo, M.-Y.; Agarwal, S. K.; Marcelin, G. K. Oxidative Coupling of Methane over Antimony-Based Catalysts. J. Catal. 1988,112, 168. Miro, E. E.; Kalenik, 2.;Santamaria, J. M.;Wolf, E. E. Transient Studies on Methane Oxidative Coupling over Alkali-Metal Promoted Titanate Catalysts. Catal. Today 1990a,6,511. Miro, E. E.; Santamaria, J. M.; Wolf, E. E. Oxidative Coupling of Methane on Alkali Metal Promoted Nickel Titanate. I. Characterization and Transient Studies. J. Catal. 1990b, 124, 451. Miro, E. E.; Santamaria, J. M.; Wolf, E. E. Oxidative Coupling of Methane on Alkali Metal Promoted Nickel Titanate. 11. Kinetic Studies. J. Catal. 199Oc,124,465. Omata, K.; Hashimoto, S.; Tominaga, H.; Fujimoto, K. Oxidative Coupling of Methane using a Membrane Reactor. Appl. Catal. 1989,52,L1. Satterfield, C. N.; Sherwood, T. K. The Role of Diffusion in Catalysis; Addison-Wesley: New York, 1963. Scurrell, M. S.Prospects for the Direct Conversion of Light Alkanes To Petrochemical Feedstocks and Liquid Fuels. A Review. Appl. Catal. 1987,32, 1. Sinev, M. Y.; Korchak, V. N.; Krylov, 0. V. Kinetic Peculiarities of Oxidative Condensation of Methane on Oxide Catalysts in a Heterogeneous-Homogeneous Process. Kinet. Catal. 1987,28, 1188. Wakao, N.; Kaguei, S. Heat and Mass Transfer in Packed Beds; Gordon & Breach: New York, 1982. Received for review November 26, 1990 Accepted January 19,1991
Multiperiod Investment Model for Processing Networks with Dedicated and Flexible Plants N. V. Sahinidis and I. E. Grossmann* Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
A processing network is modeled as a combination of dedicated and flexible production facilities. The former produce a set of products in fixed proportions at all times, while the latter can accommodate different products a t different times. Both continuous and batch operations may be involved. For such a processing network, a multiperiod mixed-integer linear programing (MILP) investment decision model is presented. The model considers the choice of technology, size of capacity additions, and allocation of resources over time in order to maximize the net present value of the project over a long-range horizon. The application of the model is illustrated with a small example.
Introduction A processing network is a combination of dedicated and flexible production facilities that are interconnected in an arbitrary manner. Dedicated production facilities produce a set of products in fixed proportions at all times and are usually used for the manufacturing of high-volume chemicals. Flexible production facilities can manufacture different products at different times and are frequently required for the manufacturing of low-volume chemicals. Both dedicated and flexible facilities can operate either continuously or in batch mode. Today most of the industrial production facilities involve continuous dedicated units; the Kellogg ammonia synthesis
* T o whom correspondence should be addressed.
process and the electrolytic production of caustic soda are just two examples. Paper mills that operate continuously and that can produce several paper types of different weight or color are examples of flexible continuous plants. Another example of flexible continuous plants are refineries that can accommodate different types of crude oils and in which the relative percentage of products changes depending on the operating conditions. Batch units have been traditionally used for the production of polymers and pharmaceuticals. Most of these batch processes are flexible since in the same unit the production can be changed to accommodate different products that need to be produced in small amounts. Dedicated batch processes can be found in the food industries where for example the production of beers,wines, and liquors requires a dedicated fermenter. Detailed descriptions of the above and other processing
0888-588519112630-1165$02.50/0 0 1991 American Chemical Society
